Distributed Newton method for time-varying convex optimization with backward Euler prediction

Zhuo Sun; Huaiming Zhu; Haotian Xu; Zhuo Sun; Huaiming Zhu; Haotian Xu

doi:10.3934/math.20241325

AIMS Mathematics

2024, Volume 9, Issue 10: 27272-27292. doi: 10.3934/math.20241325

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Research article

Distributed Newton method for time-varying convex optimization with backward Euler prediction

1.
College of Transportation Engineering, Dalian Maritime University, 116026 Dalian, China
2.
Information Science and Technology College, Dalian Maritime University, 116026 Dalian, China

Received: 27 July 2024 Revised: 28 August 2024 Accepted: 04 September 2024 Published: 20 September 2024
MSC : 49M15, 90C25

We investigated the challenge of unconstrained distributed optimization with a time-varying objective function, employing a prediction-correction approach. Our method introduced a backward Euler prediction step that used the differential information from consecutive moments to forecast the trajectory's future direction. This predicted value was then refined through an iterative correction process. Our analysis and experimental results demonstrated that this approach effectively addresses the optimization problem without requiring the computation of the Hessian matrix's inverse.
- unconstrained optimization,
- prediction-correction strategy,
- backward Euler prediction
Citation: Zhuo Sun, Huaiming Zhu, Haotian Xu. Distributed Newton method for time-varying convex optimization with backward Euler prediction[J]. AIMS Mathematics, 2024, 9(10): 27272-27292. doi: 10.3934/math.20241325

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Abstract

We investigated the challenge of unconstrained distributed optimization with a time-varying objective function, employing a prediction-correction approach. Our method introduced a backward Euler prediction step that used the differential information from consecutive moments to forecast the trajectory's future direction. This predicted value was then refined through an iterative correction process. Our analysis and experimental results demonstrated that this approach effectively addresses the optimization problem without requiring the computation of the Hessian matrix's inverse.

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